A framework is designed to represent time-varying communication networks (TVCN). We have shown the existence of window based fair end to end congestion control scheme using a multi-class fluid based model. \( (p,1) \)  proportionally fairness is used to formulate an optimization problem. According to the willingness for pay, \( (p_i) \)  of each user, an optimal window size is allocated such that congestion is minimized as well as system utility is maximized. The window-based update algorithm is proposed by considering dynamic delay especially, transmission delay \( d_{trans}(t) \) . It is observed that we are still getting a stable value of window size \( w^* \)  which is approximately same as the result obtained through La's approach [1]}. While, Mo's approach [2]} considers static delay hence, overestimates the value of optimal window size, \( W^* \) . Convergence of the proposed window-based congestion control scheme is proved by using a Lyapunov function, \( V(w) \) . For the same network topology, the converged window size, \( w^* \)  is obtained in the least amount of time through the proposed scheme. The network is time-varying therefore, User's optimal window size, \( w^* \)  is evaluated for the varying sizes of networks and we may get a different value of \( w^* \)  due to change in route of each user.
